(1) The goal of an autopilot system is to stabilize the aircraft which usually operates in 3 main equilibrium conditions: climb, cruise, and approach.

The autopilot system performs inertial X-Y-Z coordinate tracking. It is difficult to use linear equations to accurately describe the aircraft dynamics. Therefore, in the control engineering practice, we can employ state space representation to describe the dynamic behavior of an aircraft, where the Linear-Quadratic (LQ) approach is used to formulate the tracking problem of an aircraft in general.

The following project applies LQ formulation of the tracker problem in the design of an autopilot system.

Y. Chow and Y. Zheng, "Designing An Autopilot System Using The Hybrid System Approach," project report.

http://www.stanford.edu/~ychow/_pdf%20documents/AA%20690%20report.pdf 

(2) The paper [HY07] applies Linear-quadratic regulator (LQR) approach for Internet congestion control.

[HY07] Y. Hong and O.W.W. Yang, "Self-Tuning Optimal PI Rate Controller for End-to-End Congestion With LQR Approach," Proceedings of 20th International Teletraffic Congress (ITC-20), Ottawa, Canada, June 2007, pp.829-840. Available from the following RG Link.

http://www.researchgate.net/publication/221584579_Self-tuning_Optimal_PI_Rate_Controller_for_End-to-End_Congestion_With_LQR_Approach

The paper [Hong99] applies Linear-quadratic regulator (LQR) approach for servo controller design.

[Hong99] Y. Hong, “The Controller Design For Linear System: A State Space Approach,” Technical Report, National University of Singapore, November 1999. Available from the following RG link.

https://www.researchgate.net/publication/280805007_The_Controller_Design_For_Linear_System_A_State_Space_Approach

(3) Recent discussions on control system design approaches can be found in the following RG link.

"What are trends in control theory and its applications in physical systems (from a research point of view)?"

https://www.researchgate.net/post/What_are_trends_in_control_theory_and_its_applications_in_physical_systems_from_a_research_point_of_view2

Conference Paper Self-tuning Optimal PI Rate Controller for End-to-End Conges...

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Thanks for providing detailed answer